In conventional machine tools, a cutting tool, such as a turning tool, moves relative to a workpiece in a fixed direction to cut the workpiece. On the other hand, there is known a machine tool which performs so-called ultrasonic vibration cutting, which uses a piezoelectric element at a cutting edge of a cutting tool and cuts a workpiece while applying vibration in an ultrasonic range (for example, as disclosed in Japanese Published Unexamined Patent Application No. 2000-052101). Further, there is known a machine tool in which a vibration exciter is attached to a cutting tool, as disclosed in Japanese Published Examined Patent Application No. S49-17790, which will be described with reference to FIG. 13. The machine tool 100, depicted in FIG. 13, has a first guideway 101. This first guideway 101 guides a tool rest 104 coupled to a piston rod 103 of an oil hydraulic cylinder 102 so as to move perpendicular to an axial center O of a workpiece W. The machine tool 100 also has a vibration exciter 105. This vibration exciter 105 has a vibration mechanism for generating vibration in a feed direction parallel to the axial center O of the workpiece W, and a device for attachably and detachably fixing a cutting tool 106. The vibration exciter 105 is also coupled to a piston rod 108 of a feed cylinder 107 and is movable in the feed direction at a second guideway 109 fixed on the tool rest 104. By vibrating the machine tool 100 configured as above, the cutting of the workpiece W rotating about the axial center O is performed.